I examine a game-theoretical model of two variants of double-elimination tournaments, and derive the equilibrium behavior of symmetric players and the optimal prize allocation assuming a designer aims to maximize total effort. I compare these theoretical properties to the well-known single-elimination tournament. •I studied a game-theoretical model of double-elimination tournaments.•Compared to single-elimination tournaments, players have a second chance to compete.•The standard version produces higher total effort than single-elimination.•The variant version however may produce lower total effort than single-elimination.•Granting a second chance to symmetric players may create asymmetrical incentives.